Electrical Transmission Lines

• Transmission lines are specialized cables or conductors designed to efficiently carry alternating current (AC) electrical power over long distances with minimal energy loss.
• They form a critical component of electrical grids, connecting power plants to substations and distribution networks.
• Their design and operation require consideration of various electrical parameters, including impedance matching, voltage regulation, and power loss minimization.

Types of Transmission Lines

• Overhead lines: Suspend conductors in the air using towers or poles.
• Underground cables: Buried beneath the surface, offering advantages in aesthetics and weather resilience.
• Both types have distinct characteristics, applications, and cost considerations.

Key Parameters

• Characteristic Impedance (Z0): The ratio of voltage to current when a wave travels along the line in one direction, crucial for impedance matching to prevent reflections.
• Propagation Constant (γ): A measure of how much the signal changes (both in amplitude and phase) as it travels down the line per unit length. It comprises the attenuation constant (α) and phase constant (β).
• Attenuation Constant (α): Represents the signal loss per unit length, measured in nepers per meter (Np/m) or decibels per meter (dB/m).
• Phase Constant (β): Indicates the phase shift per unit length, measured in radians per meter (rad/m).
• Velocity of Propagation (v): The speed at which the electromagnetic wave travels along the line, often a fraction of the speed of light.

Transmission Line Models

• Transmission lines are modeled using distributed parameters due to their length relative to the wavelength of the signal.
• These models consider resistance (R), inductance (L), capacitance (C), and conductance (G) distributed uniformly along the line's length.
• Short Line Model: Used when the line length is much smaller than the wavelength (e.g., < 5% of λ). Only series impedance (R + jωL) is considered, and shunt capacitance is ignored.
• Medium Line Model: Applicable for lines with moderate lengths (e.g., 5-80% of λ). Includes series impedance and shunt capacitance, which is lumped at one or more points along the line (e.g., nominal π or T models).
• Long Line Model: Necessary when the line length is comparable to or greater than the wavelength (e.g., > 80% of λ). Uses distributed parameters and hyperbolic functions to accurately represent voltage and current variations along the line.

Power Flow

• Power flow through transmission lines is governed by the voltage magnitude and phase angle differences between the sending and receiving ends.
• Real power (P) and reactive power (Q) flow are key considerations in power system analysis.
• Surge Impedance Loading (SIL): The power delivered to a load impedance equal to the characteristic impedance of the line. At SIL, the voltage profile along the line is flat, and reactive power losses are minimized.

Voltage Regulation

• Voltage regulation is the measure of voltage drop from the sending end to the receiving end under load conditions.
• It is expressed as a percentage of the receiving-end voltage.
• Poor voltage regulation can lead to equipment malfunction and instability.
• Compensation techniques, such as using tap-changing transformers, shunt capacitors, or synchronous condensers, are employed to maintain voltage within acceptable limits.

Losses

• Transmission line losses include both resistive (I²R) losses in the conductors and dielectric losses in the insulation.
• Corona loss: Occurs due to ionization of the air surrounding the conductors at high voltages, leading to power dissipation and audible noise.
• Minimizing losses is essential for efficient power transmission.
• High-voltage direct current (HVDC) transmission can reduce losses over very long distances compared to AC transmission.

Surge Impedance

• Surge impedance (Z0) is a characteristic property of a transmission line, defined as the ratio of voltage to current for a traveling wave.
• It is determined by the line's inductance (L) and capacitance (C) per unit length (Z0 = √(L/C)).
• Surge impedance loading (SIL) represents the power level at which the reactive power generated by the line's capacitance is equal to the reactive power absorbed by the line's inductance.

Reflection

• Reflections occur when a transmission line is not properly terminated, leading to signal distortion and power loss.
• If the load impedance (ZL) is not equal to the characteristic impedance (Z0), a portion of the incident wave is reflected back towards the source.
• The reflection coefficient (Γ) quantifies the magnitude and phase of the reflected wave relative to the incident wave (Γ = (ZL - Z0) / (ZL + Z0)).
• Standing waves: Voltage and current patterns that result from the interference of incident and reflected waves.

Standing Wave Ratio

• Standing Wave Ratio (SWR): the ratio of the maximum voltage to the minimum voltage along the line.
• SWR indicates the degree of impedance matching between the transmission line and the load.
• A SWR of 1:1 indicates perfect matching, while higher SWR values indicate greater impedance mismatch and increased reflections.

Impedance Matching Techniques

• Impedance matching is critical for efficient power transfer and minimizing signal reflections.
• Techniques include using stub matching, quarter-wave transformers, and impedance matching networks.
• Stub Matching: Involves connecting a shorted or open-circuited transmission line (stub) in parallel with the main line at a specific distance from the load to cancel out the reactive component of the load impedance.
• Quarter-Wave Transformer: A transmission line with a length of one-quarter wavelength (λ/4) and a characteristic impedance equal to the geometric mean of the source and load impedances (Z = √(ZS * ZL)).

Transients

• Transients are temporary surges in voltage or current caused by switching operations, faults, or lightning strikes.
• They can damage equipment and disrupt system operation.
• Surge arresters and other protective devices are used to mitigate the effects of transients.
• Bewley Lattice Diagram: A graphical tool used to analyze transient behavior on transmission lines, tracking voltage and current waves as they propagate and reflect along the line.

Corona Effect

• Corona is a phenomenon that occurs when the electric field strength around a conductor exceeds the dielectric strength of the surrounding air.
• It results in ionization of the air, producing a faint bluish glow, audible noise, and radio interference.
• Corona loss is a form of power loss and can also degrade insulators over time.
• Factors affecting corona include voltage level, conductor size and spacing, air density, and surface condition of the conductor.

Bundled Conductors

• Bundled conductors consist of multiple conductors per phase, arranged in a specific geometric configuration.
• They reduce corona effect by decreasing the electric field strength at the conductor surface.
• Bundling also increases the transmission line's capacity and reduces inductance.
• The increased capacitance leads to a higher surge impedance loading (SIL) and improved voltage stability.

Sag and Tension

• Sag: The vertical distance between the highest point of a suspended conductor and the straight line connecting the two support points.
• Tension: The mechanical force exerted on the conductor.
• Sag and tension are important considerations in overhead line design to ensure adequate ground clearance and structural integrity.
• Factors affecting sag include conductor weight, temperature, wind and ice loading, and span length.